Search results for "Applied Mathematics"
showing 10 items of 4379 documents
A probabilistic approach to radiant field modeling in dense particulate systems
2016
Radiant field distribution is an important modeling issue in many systems of practical interest, such as photo-bioreactors for algae growth and heterogeneous photo-catalytic reactors for water detoxification.In this work, a simple radiant field model suitable for dispersed systems showing particle size distributions, is proposed for both dilute and dense two-phase systems. Its main features are: (i) only physical, independently assessable parameters are involved and (ii) its simplicity allows a closed form solution, which makes it suitable for inclusion in a complete photo-reactor model, where also kinetic and fluid dynamic sub-models play a role. A similar model can be derived by making us…
Nonexistence Results for Higher Order Fractional Differential Inequalities with Nonlinearities Involving Caputo Fractional Derivative
2021
Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the nonexistence of global solutions to a higher order fractional differential inequality with a nonlinearity involving Caputo fractional derivative. Namely, using nonlinear capacity estimates, we obtain sufficient conditions for which we have no global solutions. The a priori estimates of the structure of solutions are obtained by a precise analysis …
Gradient estimates for solutions to quasilinear elliptic equations with critical sobolev growth and hardy potential
2015
This note is a continuation of the work \cite{CaoXiangYan2014}. We study the following quasilinear elliptic equations \[ -\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u=Q(x)|u|^{\frac{Np}{N-p}-2}u,\quad\, x\in\mathbb{R}^{N}, \] where $1<p<N,0\leq\mu<\left((N-p)/p\right)^{p}$ and $Q\in L^{\infty}(\R^{N})$. Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.
Rates of convergence to equilibrium for collisionless kinetic equations in slab geometry
2017
This work deals with free transport equations with partly diffuse stochastic boundary operators in slab geometry. Such equations are governed by stochastic semigroups in $L^{1}$ spaces$.\ $We prove convergence to equilibrium at the rate $O\left( t^{-\frac{k}{2(k+1)+1}}\right) \ (t\rightarrow +\infty )$ for $L^{1}$ initial data $g$ in a suitable subspace of the domain of the generator $T$ where $k\in \mathbb{N}$ depends on the properties of the boundary operators near the tangential velocities to the slab. This result is derived from a quantified version of Ingham's tauberian theorem by showing that $F_{g}(s):=\lim_{\varepsilon \rightarrow 0_{+}}\left( is+\varepsilon -T\right) ^{-1}g$ exists…
The Performance of the Gradient-Like Influence Measure in Generalized Linear Mixed Models
2015
A gradient-like statistic, recently introduced as an influence measure, has been proven to work well in large sample, thanks to its asymptotic properties. In this work, through small-scale simulation schemes, the performance of such a diagnostic measure is further investigated in terms of concordance with the main influence measures used for outlier identification. The simulation studies are performed by using generalized linear mixed models (GLMMs).
A thermodynamically consistent cohesive-frictional interface model for mixed mode delamination
2016
Abstract A new interface constitutive model based on damage mechanics and frictional plasticity is presented. The model is thermodynamically consistent, it is able to accurately reproduce arbitrary mixed mode debonding conditions and it is proved that the separation work is always bounded between the fracture energy in mode I and the fracture energy in mode II. Analytical results are given for proportional loading paths and for two non-proportional loading paths, confirming the correct behavior of the model for complex loading histories. Numerical and analytical solutions are compared for three classical delamination tests and frictional effects on 4ENF are also considered.
Free energy and states of fractional-order hereditariness
2014
AbstractComplex materials, often encountered in recent engineering and material sciences applications, show no complete separations between solid and fluid phases. This aspect is reflected in the continuous relaxation time spectra recorded in cyclic load tests. As a consequence the material free energy cannot be defined in a unique manner yielding a significative lack of knowledge of the maximum recoverable work that can extracted from the material. The non-uniqueness of the free energy function is removed in the paper for power-laws relaxation/creep function by using a recently proposed mechanical analogue to fractional-order hereditariness.
Effects of mechanical deformation on electronic transport through multiwall carbon nanotubes
2017
Abstract The effects of mechanical deformation on the electron transport behavior of carbon nanotubes (CNTs) are of primary interest due to the enormous potential of nanotubes in making electronic devices and nanoelectromechanical systems (NEMS). Moreover it could help to evaluate the presence of defects or to assess the type of CNTs that were produced. Conventional atomistic simulations have a high computational expense that limits the size of the CNTs that can be studied with this technique and a direct analysis of CNTs of the dimension used in nano-electronic devices seems prohibitive at the present. Here a novel approach was designed to realize orders-of-magnitude savings in computation…
On the measurement of local gas hold-up, interfacial area and bubble size distribution in gas–liquid contactors via light sheet and image analysis: I…
2013
Abstract In this work a novel experimental technique for measuring local gas hold-up, interfacial area and bubble size distribution, in gas–liquid systems is proposed. The technique is based on advanced Image Processing coupled with experimental set-ups typically available for Particle Image Velocimetry. A fluorescent dye dissolved in the liquid phase allows to identify in-plane bubbles among all visible bubbles in the images. To this end, a suitable algorithm is proposed. The raw data so obtained are processed by previously developed statistical methods that result in a reliable reconstruction of actual dispersion properties. The technique is applied to the case of a gas-dispersed mechanic…
The global cracking laws for a finite-element model of no-tension material
1992
Abstract For perfect no-tension materials (NRT) the validity of the local stability postulate of Drucker, well known in plasticity, has been assumed so far and utilized to derive the local cracking laws, which relate cracking strain states and stress states to each other. On this base a finite-element (FE) model with suitable constitutive behaviour for the single FE is presented. Classical FE approaches enforce the cracking laws at the Gauss points of the FEs. In this work it is shown that taking into account cracking strains, suitably modelled, over the whole domain of the FE and making use of an energy approach lead to general cracking laws describing the constitutive behaviour of the who…